state_inherited.dart

import 'package:flutter/widgets.dart';

void main() => runApp(TopWidget());

class CounterInherited extends InheritedWidget {
  CounterInherited({
    Key key,
    @required this.state,
    @required Widget child,
  }) : super(key: key, child: child);

  final _TopWidgetState state;

  @override
  bool updateShouldNotify(CounterInherited old) => true;

  static CounterInherited of(BuildContext context) =>
      context.dependOnInheritedWidgetOfExactType<CounterInherited>();
}

class TopWidget extends StatefulWidget {
  @override
  _TopWidgetState createState() => _TopWidgetState();
}

class _TopWidgetState extends State<TopWidget> {
  int counter = 0;

  void increment() {
    setState(() {
      counter++;
    });
  }

  @override
  Widget build(BuildContext context) {
    return MaterialApp(
      home: CounterInherited(
        state: this,
        child: MiddleWidget(),
      ),
    );
  }
}

class MiddleWidget extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return Scaffold(
      body: BottomWidget(),
    );
  }
}

class BottomWidget extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    final int counter = CounterInherited.of(context).state.counter;

    return Container(
      child: Text(counter.toString()),
    );
  }
}